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On a Class of Parametric (p, 2)-equations

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Abstract

We consider parametric equations driven by the sum of a p-Laplacian and a Laplace operator (the so-called (p, 2)-equations). We study the existence and multiplicity of solutions when the parameter \(\lambda >0\) is near the principal eigenvalue \(\hat{\lambda }_1(p)>0\) of \((-\Delta _p,W^{1,p}_{0}(\Omega ))\). We prove multiplicity results with precise sign information when the near resonance occurs from above and from below of \(\hat{\lambda }_1(p)>0\).

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Acknowledgments

V.D. Rădulescu was partially supported by the Romanian Research Council through the Grant CNCS-UEFISCDI-PCCA-23/2014. D.D. Repovš acknowledges the partial support of the Slovenian Research Agency through Grants P1-0292-0101, J1-7025-0101 and J1-6721-0101.

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Authors and Affiliations

  1. Department of Mathematics, National Technical University, Zografou Campus, 15780, Athens, Greece

    Nikolaos S. Papageorgiou

  2. Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Vicenţiu D. Rădulescu

  3. Department of Mathematics, University of Craiova, 200585, Craiova, Romania

    Vicenţiu D. Rădulescu

  4. Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, Kardeljeva ploščad 16, 1000, Ljubljana, Slovenia

    Dušan D. Repovš

Authors
  1. Nikolaos S. Papageorgiou
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  2. Vicenţiu D. Rădulescu
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  3. Dušan D. Repovš
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Correspondence to Vicenţiu D. Rădulescu.

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Papageorgiou, N.S., Rădulescu, V.D. & Repovš, D.D. On a Class of Parametric (p, 2)-equations. Appl Math Optim 75, 193–228 (2017). https://doi.org/10.1007/s00245-016-9330-z

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